CN109905158A - The design method of even power broadband signal Adaptive beamformer best initial weights - Google Patents
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Abstract
The design method of even power broadband signal Adaptive beamformer best initial weights, the present invention relates to the design methods of self-adaptive numerical integration algorithm best initial weights.The purpose of the present invention is to solve existing for broadband signal, when bandwidth is very big, will affect the beam position of Wave beam forming, and influences adaptive interference mitigation direction, leads to the problem that angular error is big.Detailed process are as follows: Step 1: expression formula of the building even power broadband signal in General Cell；Step 2: expression formula of the even power broadband signal in General Cell in step 1 is applied in uniform rectilinear phased array, the covariance matrix of useful signal, interference signal, noise signal is obtained；Step 3: the covariance matrix of useful signal, interference signal obtained in step 2, noise signal is substituted into linearly constrained minimum variance, optimal adaptive weight is obtained.The present invention is used for the field of broadband signal Adaptive beamformer best initial weights design.
Description
Technical field
The present invention relates to the design methods of self-adaptive numerical integration algorithm best initial weights.
Background technique
Digital phase control array radar is by digital technology and antenna technology perfect combination, with number under transmitting and reception pattern
Wave beam forming (Digital Beam Forming, DBF) replaces traditional analog beam to be formed, and it is incomparable to possess conventional radar
Advantage.It is anti-dry to the resolution of target, raising radar in order to obtain High Range Resolution, high range accuracy, raising radar simultaneously
The problems such as disturbing, transmitting signal will be using the signals of big instant bandwidth.If phased-array radar use broadband signal, function and
Performance can improve a lot.Such as broadband signal is used in early warning plane, the interference free performance of early warning plane can be greatly improved,
Improve detectivity of the early warning plane under strong jamming.Meanwhile broadband can provide more target informations, realize air detection and
Detection combines over the ground, target acquisition and multiple target tracking combine.
Existing technology is primarily adapted for use in narrow band signal, thinks signal bandwidth B than carrier frequency f in narrow band signal0Small is more,
Ignore difference of the signal envelope in each array element in practical application；Further, since signal bandwidth is smaller, Wave beam forming will not influence
Direction and adaptive interference mitigation be directed toward angle.But for broadband signal, difference of the signal envelope in each array element
Different to ignore, when bandwidth is very big, beam position and the adaptive interference mitigation error in pointing that will cause directional diagram are big.Work as letter
Number be carrier frequency f0When=1.6GHZ, bandwidth B=200MHZ broadband signal, frequency f is f0- B/2, f0, f0Beam direction when+B/2
Figure is as shown in Figure 1.
From figure 1 it appears that its main beam deviation be 6 ° or so, adaptive interference mitigation differ 10 ° or so, cause compared with
Big error.
Summary of the invention
The purpose of the present invention is to solve the prior arts for broadband signal, when bandwidth is very big, the side of will cause
The problem big to the beam position and adaptive interference mitigation error in pointing of figure, and propose the adaptive wave of even power broadband signal
The design method of beam formation best initial weights.
The design method detailed process of even power broadband signal Adaptive beamformer best initial weights are as follows:
Step 1: expression formula of the building even power broadband signal in General Cell；
Step 2: expression formula of the even power broadband signal in General Cell in step 1 is applied to uniform rectilinear phase
It controls in battle array, obtains the covariance matrix of useful signal, interference signal, noise signal；
Step 3: the covariance matrix of useful signal, interference signal obtained in step 2, noise signal is substituted into linear
It constrains in minimum variance principle, obtains optimal adaptive weight.
The invention has the benefit that
The present invention makes directional diagram using self-adaptive numerical integration algorithm technology in the receiving end of digital phase control array 1 system
Beam position and adaptive interference mitigation error in pointing reduce, and complete the self-adaptive numerical integration algorithm of broadband signal.
It may be implemented to carry out adaptive digital wave beam to even power broadband signal in the receiving end of the Digital Phased Array radar
It is formed, and forms adaptive nulling in interference radiating way, reduce the beam position of directional diagram and adaptive interference mitigation error.
Fig. 2 is it can be seen from the figure that wave beam is all directed to signal arrival bearing, and to be done using the beam pattern after the present invention
The null error for disturbing direction, which can be ignored, not to be remembered, there is preferable correction effect.
As shown in embodiment one, existing its main beam of Narrow bands Wave beam forming is respectively directed to 27 °, and 30 °, 33 °, maximum is partially
Difference is 6 ° or so, and at 45 °, 50 °, 55 ° of formation disturbance nulls, maximum deviation is 10 ° or so.
Its main beam of the method for the present invention Wave beam forming is all directed to 30 °, at 49 °, 50 °, 51 ° of formation disturbance nulls, effectively
Ground forms broadband beams, and 6 ° or so of main beam improvement, disturbance null improve 10 ° or so.
Detailed description of the invention
Fig. 1 is beam pattern；
Fig. 2 is the modified beam pattern of the present invention；
Fig. 3 is Homogeneous linear array of figure of the present invention；
Fig. 4 is that Homogeneous linear of the present invention receives phased array figure；
Fig. 5 is the optimal adaptive weight w flow chart of the present invention.
Specific embodiment
Specific embodiment 1: the design of present embodiment even power broadband signal Adaptive beamformer best initial weights
Method detailed process are as follows:
Step 1: expression formula of the building even power broadband signal in General Cell；
Step 2: expression formula of the even power broadband signal in General Cell in step 1 is applied to uniform rectilinear phase
It controls in battle array, obtains the covariance matrix of useful signal, interference signal, noise signal；
Step 3: the covariance matrix of useful signal, interference signal obtained in step 2, noise signal is substituted into linear
It constrains in minimum variance principle, obtains optimal adaptive weight.
Specific embodiment 2: the present embodiment is different from the first embodiment in that, it is constructed in the step 1 equal
Expression formula of the even power wide-band signal in General Cell；Detailed process are as follows:
Assuming that even power wideband signal source is s (t), even power broadband signal bandwidth is B, even power broadband signal
Centre frequency be f0, and the power spectral density obedience of s (t) is uniformly distributed, i.e., the power spectral density function of signal s (t) is ps
(f)；
If having in an array (this array can be any array, the array of uniform power spectrum density broadband signal) N number of
Array element, first array element are located at rectangular coordinate system origin, and any one array element coordinate can be expressed as z in arrayi=(xi,yi),
Wherein i=1,2 ..., N, xiFor the abscissa of array element, yiFor the ordinate of array element；
When wideband signal source s (t) is in far field, θ is direction of propagation angle, then beam vectors can be expressed as u=(cos
θ,sinθ)T；
Wherein, T is transposition；
Then any delay time T of the array element relative to first array element in this arrayi=(ziU) (dot product is /c
xicosθ+yiSin θ), i=1,2 ..., N, so even power broadband signal be incident on each array element and first array element when
Between difference be τ=[τ1,…,τi,…,τN], i=1,2 ..., N；
In formula, c is the light velocity；
When noise is not present, the output signal of i-th of array element is expressed as
yi(t)=si(t-τi) i=1,2 ..., N (2)
In formula, si(t-τi) it is the expression formula that wideband signal source is incident on i-th of array element；
Even power broadband signal output vector after array is y (t)=[y at this time1(t),…,yi(t),…,yN
(t)], wherein because s (t) is even power wideband signal source, y (t) is expressed as with carat is silent
In formula, y1It (t) is the output of first array element of array, yiIt (t) is the output of i-th of array element of array, yNIt (t) is battle array
The output of column n-th array element, n are variable, and m is variable, and j is imaginary number, j2=-1；
(3) formula is write as baseband form and is then expressed as
Even power broadband signal is divided into L cross-talk frequency band in bandwidth B, each sub-band is weighted respectively, then
(4) formula can be write as
Wherein nlFor the frequency of l cross-talk frequency band；wlFor the weight of l cross-talk frequency band.
Other steps and parameter are same as the specific embodiment one.
Specific embodiment 3: the present embodiment is different from the first and the second embodiment in that, the signal s (t)
Power spectral density function ps(f) expression formula are as follows:
Wherein, t is time variable, ps(f) power spectral density function for being signal s (t), f are frequency variable, and p is signal s
(t) power spectral density.
Other steps and parameter are the same as one or two specific embodiments.
Specific embodiment 4: unlike one of present embodiment and specific embodiment one to three, the l cross-talk
The frequency of frequency band
Other steps and parameter are identical as one of specific embodiment one to three.
Specific embodiment 5: unlike one of present embodiment and specific embodiment one to four, the l cross-talk
The weight w of frequency bandl=0.5-0.5cos (2 π l/L-1), l=1,2 ..., L.
Other steps and parameter are identical as one of specific embodiment one to four.
Specific embodiment 6: unlike one of present embodiment and specific embodiment one to five, the step 2
It is middle to apply to expression formula of the even power broadband signal in General Cell in step 1 in uniform rectilinear phased array, had
With signal, the covariance matrix of interference signal, noise signal；Detailed process are as follows:
So the covariance matrix of broadband useful signal can be expressed as
R1=E [d (t- τ) d (t- τ)H] (13)
The covariance matrix of wideband interferer signal can be expressed as
R2=E [k (t- τ) k (t- τ)H] (14)
The covariance matrix of noise signal n (t) can be expressed as
Rn=E [n (t) n (t)H] (15)
Wherein, E [] is covariance matrix, and H is conjugate transposition；D (t- τ) is the useful signal that all array elements of array receive
The n dimensional vector n of the M constituted × 1, the n dimensional vector n of M × 1 that the interference signal that k (t- τ) is received by all array elements of array is constituted, n
It (t) is array element grade Gauss additive white noise.
Other steps and parameter are identical as one of specific embodiment one to five.
Specific embodiment 7: unlike one of present embodiment and specific embodiment one to six, the useful letter
Number, the specific solution procedure of covariance matrix of interference signal, noise signal are as follows:
Uniform rectilinear phased array is used in the present invention, is equipped with a M array element Homogeneous linear array structure as shown in figure 3, each
Bay is that omnidirectional's array element is located in rectangular coordinate system X-axis, and first array element at origin is reference array element, and is appointed
Adjacent two array element spacing of anticipating is d, wherein λ/2 d=, and array length is L=(M-1) d；λ is signal wavelength；
For Homogeneous linear array, one-dimensional scanning can only be completed in pitch angle, azimuth is not scanned, so only closing
Directional diagram on the direction heart θ.
In view of there are a broadband useful signal d (t) and a wideband interferer signal k (t), useful signal and interference in far field
Signal is respectively with θdAnd θkAngle is incident on each array element simultaneously, and the space delay distance of two array element of arbitrary neighborhood is on linear array
Δ=d sin θd, corresponding delay time T=d sin θd/ c, thus useful signal and interference signal be incident on each array element with
The time difference of reference array element is τ=[τ1,…,τi,…,τM], i=1,2 ..., M；(the time of useful signal and interference signal
Difference is identical)
D is array element spacing；
At this point, the output of array element is
X (t)=[x1(t),…,xi(t),…,xM(t)]T (6)
Wherein
X (t)=d (t- τ)+k (t- τ)+n (t) (7)
Wherein, x1It (t) is first array element received signal of array, xiIt (t) is i-th of array element received signal of array, xM
It (t) is array m-th array element received signal, M × 1 that the useful signal that d (t- τ) is received by all array elements of array is constituted
N dimensional vector n, the n dimensional vector n of M × 1 that the interference signal that k (t- τ) is received by all array elements of array is constituted, n (t) are that array element grade is high
This additive white noise, the noise in each channel is mutually indepedent, and the signal in different array elements is also mutually indepedent；
It is exactly that y (t) represents the expression formula after General Cell receiving wide-band signal, this expression formula can represent any width
Band signal (premise power is uniform) and any array, are broad sense, and x (t) is specific to broad sense above, specially line array
Column, and array simultaneously receiving wide-band signal, broadband interference and noise, be exactly in fact above y (t) expression under normal circumstances
, and x (t) is indicated under actual conditions；
I.e.
D (t- τ)=[d (t- τ1),…,d(t-τi),…,d(t-τN)]T (8)
K (t- τ)=[k (t- τ1),…,k(t-τi),…,k(t-τN)]T (9)
N (t)=[n1(t),…,ni(t),…,nN(t)]T (10)
Wherein, d (t- τ1) for first received useful signal of array element of array, d (t- τi) for i-th of array element institute of array
Received useful signal, d (t- τM) for the received useful signal of array m-th array element, k (t- τ1) it is first array element of array
The received interference signal of institute, k (t- τi) for the received interference signal of i-th of array element of array, k (t- τN) it is array m-th array element
The received interference signal of institute, n1It (t) is first received noise signal of array element of array, niIt (t) is i-th of array element institute of array
Received noise signal, nMIt (t) is the received noise signal of array m-th array element；
D (t- τ), k (t- τ) signal are all broadband signal, can be expressed as
Wherein, wqFor the weight of q cross-talk frequency band, q=1,2 ..., Q, Q is the sub-band number of interference signal, f1It is dry
Disturb the carrier frequency of signal k (t), nqFor the frequency of q cross-talk frequency band,
Expression formula of the even power broadband signal in General Cell in step 1It is suitable for
Any situation, step 2 according toThe M that the useful signal that all array elements of array receive is constituted
× 1 n dimensional vector n d (t- τ) is expressed as d (t- τ)=[d (t- τ1),…,d(t-τi),…,d(t-τN)]T, all array elements receptions of array
To the n dimensional vector n of M × 1 k (t- τ) that is constituted of interference signal be expressed as k (t- τ)=[k (t- τ1),…,k(t-τi),…,k(t-
τN)]T, array element grade Gauss additive white noise n (t) is expressed as n (t)=[n1(t),…,ni(t),…,nN(t)]T；
So the covariance matrix of broadband useful signal can be expressed as
R1=E [d (t- τ) d (t- τ)H] (13)
The covariance matrix of wideband interferer signal can be expressed as
R2=E [k (t- τ) k (t- τ)H] (14)
The covariance matrix of noise signal n (t) can be expressed as
Rn=E [n (t) n (t)H] (15)
Wherein, E [] is covariance matrix, and H is conjugate transposition；
Other steps and parameter are identical as one of specific embodiment one to six.
Specific embodiment 8: unlike one of present embodiment and specific embodiment one to seven, the step 3
The middle covariance matrix by useful signal, interference signal obtained in step 2, noise signal substitutes into linear constraint minimal variance
In criterion, optimal adaptive weight is obtained；Detailed process are as follows:
The design of adaptive weight
Receiving array is as shown in figure 4, wherein the phase shifter of each array element is for controlling beam position.Adaptively to inhibit dry
It disturbs, signal need to be weighted, design adaptive weight uses LCMV (Linearly Constrained in the present invention
Minimum Variance, linear constraint minimal variance) criterion；Signal to Interference plus Noise Ratio (signal and the interference for namely exporting system
The power ratio of plus noise) it is maximum, that is, there is optimal adaptive interference mitigation performance.
If the beam position of array is θ0, optimal adaptive weight vector w is the column vector of M dimension, optimal adaptive power
Vector w is based on LCMV criterion and obtains, i.e.,
Wherein μ is any one constant；α(f,θ0) be array guiding vector；
It enablesWhereinFor spherical wave received by i-th of array element,
F is working frequency, then
It is the valuation of the interference plus noise covariance matrix of array output, is M × M dimension square matrix,It is done by broadband
The covariance matrix of the covariance matrix plus noise n (t) disturbed carries out K sampling and is estimated to obtain, expression formula are as follows:
Wherein K is sampling number, by α (f, θ0) andFormula (16) is brought into get uniform power spectrum density broadband signal number is arrived
The optimal adaptive weight w of word Wave beam forming.
In the present invention, determine that the flow chart of optimal adaptive weight w is as shown in Figure 5.
Other steps and parameter are identical as one of specific embodiment one to seven.
Beneficial effects of the present invention are verified using following embodiment:
Embodiment one: as follows using parameter in emulation: the total array number 32 of even linear array, useful signal centre frequency f0=
1.6GHz, bandwidth 200MHz, for array using uniformly weighting, arrival bearing is 30 °, and it is 200MHz that bandwidth, which is added, in 50 ° of directions
Interference signal, for estimate covariance matrix in adaptive algorithm, it is assumed that data sampling points be 100.
Existing its main beam of Narrow bands Wave beam forming is respectively directed to 27 °, and 30 °, 33 °, maximum deviation is 6 ° or so,
45 °, 50 °, 55 ° of formation disturbance nulls, maximum deviation is 10 ° or so.
Its main beam of the method for the present invention Wave beam forming is all directed to 30 °, at 49 °, 50 °, 51 ° of formation disturbance nulls, effectively
Ground forms broadband beams, and 6 ° or so of main beam improvement, disturbance null improve 10 ° or so.
The present invention can also have other various embodiments, without deviating from the spirit and substance of the present invention, this field
Technical staff makes various corresponding changes and modifications in accordance with the present invention, but these corresponding changes and modifications all should belong to
The protection scope of the appended claims of the present invention.
Claims (8)
1. the design method of even power broadband signal Adaptive beamformer best initial weights, it is characterised in that: the method tool
Body process are as follows:
Step 1: expression formula of the building even power broadband signal in General Cell；
Step 2: expression formula of the even power broadband signal in General Cell in step 1 is applied to uniform rectilinear phased array
In, obtain the covariance matrix of useful signal, interference signal, noise signal；
Step 3: the covariance matrix of useful signal, interference signal obtained in step 2, noise signal is substituted into linear restriction
In minimum variance principle, optimal adaptive weight is obtained.
2. the design method of even power broadband signal Adaptive beamformer best initial weights according to claim 1, special
Sign is: expression formula of the even power broadband signal in General Cell is constructed in the step 1；Detailed process are as follows:
Assuming that even power wideband signal source is s (t), even power broadband signal bandwidth is B, in even power broadband signal
Frequency of heart is f0, and the power spectral density obedience of s (t) is uniformly distributed, i.e., the power spectral density function of signal s (t) is ps(f)；
If there is N number of array element in an array, first array element is located at rectangular coordinate system origin, any one array element coordinates table in array
It is shown as zi=(xi,yi),
Wherein i=1,2 ..., N, xiFor the abscissa of array element, yiFor the ordinate of array element；
When wideband signal source s (t) is in far field, θ is direction of propagation angle, then beam vectors are expressed as u=(cos θ, sin θ)T；
Wherein, T is transposition；
Then any delay time T of the array element relative to first array element in this arrayi=(ziU)/c, i=1,2 ..., N, so
It is τ=[τ that even power broadband signal, which is incident on each array element and the time difference of first array element,1,…,τi,…,τN], i=1,
2,…,N；
In formula, c is the light velocity；
When noise is not present, the output signal of i-th of array element is expressed as
yi(t)=si(t-τi) i=1,2 ..., N (2)
In formula, si(t-τi) it is the expression formula that wideband signal source is incident on i-th of array element；
Even power broadband signal output vector after array is y (t)=[y at this time1(t),…,yi(t),…,yN(t)],
In because s (t) is even power wideband signal source, y (t) is expressed as with carat is silent
In formula, y1It (t) is the output of first array element of array, yiIt (t) is the output of i-th of array element of array, yNIt (t) is array N
The output of a array element, n are variable, and m is variable, and j is imaginary number, j2=-1；
(3) formula is write as baseband form and is then expressed as
Even power broadband signal is divided into L cross-talk frequency band in bandwidth B, each sub-band is weighted respectively, then (4) formula
It is write as
Wherein nlFor the frequency of l cross-talk frequency band；wlFor the weight of l cross-talk frequency band.
3. the design method of even power broadband signal Adaptive beamformer best initial weights according to claim 2, special
Sign is: the power spectral density function of the signal s (t) is ps(f)；
Wherein, t is time variable, ps(f) power spectral density function for being signal s (t), f are frequency variable, and p is signal s's (t)
Power spectral density.
4. the design method of even power broadband signal Adaptive beamformer best initial weights according to claim 3, special
Sign is: the frequency of the l cross-talk frequency band
5. the design method of even power broadband signal Adaptive beamformer best initial weights according to claim 4, special
Sign is: the weight w of the l cross-talk frequency bandl=0.5-0.5cos (2 π l/L-1), l=1,2 ..., L.
6. the design method of even power broadband signal Adaptive beamformer best initial weights according to claim 5, special
Sign is: applying to expression formula of the even power broadband signal in General Cell in step 1 uniformly directly in the step 2
In line phased array, the covariance matrix of useful signal, interference signal, noise signal is obtained；Detailed process are as follows:
So the covariance matrix of broadband useful signal is expressed as
R1=E [d (t- τ) d (t- τ)H] (13)
The covariance matrix of wideband interferer signal is expressed as
R2=E [k (t- τ) k (t- τ)H] (14)
The covariance matrix of noise signal n (t) is expressed as
Rn=E [n (t) n (t)H] (15)
Wherein, E [] is covariance matrix, and H is conjugate transposition；The useful signal institute structure that d (t- τ) receives for all array elements of array
At the n dimensional vector n of M × 1, the n dimensional vector n of M × 1 that the interference signal that k (t- τ) is received by all array elements of array is constituted, n (t) is
Array element grade Gauss additive white noise.
7. the design method of even power broadband signal Adaptive beamformer best initial weights according to claim 6, special
Sign is: the useful signal, interference signal, the specific solution procedure of covariance matrix of noise signal are as follows:
Equipped with a M array element Homogeneous linear array, each bay is that omnidirectional's array element is located in rectangular coordinate system X-axis, is located at
First array element at origin is reference array element, and two array element spacing of arbitrary neighborhood is d, wherein d=λ 2, array length L
=(M-1) d；λ is signal wavelength；
There are a broadband useful signal d (t) and a wideband interferer signal k (t) in far field, useful signal and interference signal respectively with
θdAnd θkAngle is incident on each array element simultaneously, and the space delay distance of two array element of arbitrary neighborhood is Δ=dsin θ on linear arrayd,
Corresponding delay time T=d sin θd/ c, so useful signal and interference signal are incident on each array element and reference array element
Time difference is τ=[τ1,…,τi,…,τM], i=1,2 ..., M；
D is array element spacing；
At this point, the output of array element is
X (t)=[x1(t),…,xi(t),…,xM(t)]T (6)
Wherein
X (t)=d (t- τ)+k (t- τ)+n (t) (7)
Wherein, x1It (t) is first array element received signal of array, xiIt (t) is i-th of array element received signal of array, xM(t)
For array m-th array element received signal, the M × 1 that the useful signal that d (t- τ) is received by all array elements of array is constituted is tieed up
Vector, the n dimensional vector n of M × 1 that the interference signal that k (t- τ) is received by all array elements of array is constituted, n (t) are array element grade Gausses
Additive white noise；
I.e.
D (t- τ)=[d (t- τ1),…,d(t-τi),…,d(t-τN)]T (8)
K (t- τ)=[k (t- τ1),…,k(t-τi),…,k(t-τN)]T (9)
N (t)=[n1(t),…,ni(t),…,nN(t)]T (10)
Wherein, d (t- τ1) for first received useful signal of array element of array, d (t- τi) received by i-th of array element of array
Useful signal, d (t- τM) for the received useful signal of array m-th array element, k (t- τ1) connect by first array element of array
The interference signal of receipts, k (t- τi) for the received interference signal of i-th of array element of array, k (t- τN) connect by array m-th array element
The interference signal of receipts, n1It (t) is first received noise signal of array element of array, ni(t) it is received by i-th of array element of array
Noise signal, nMIt (t) is the received noise signal of array m-th array element；
D (t- τ), k (t- τ) signal are all broadband signal, are expressed as
Wherein, wqFor the weight of q cross-talk frequency band, q=1,2 ..., Q, Q is the sub-band number of interference signal, f1For interference letter
The carrier frequency of number k (t), nqFor the frequency of q cross-talk frequency band,
So the covariance matrix of broadband useful signal is expressed as
R1=E [d (t- τ) d (t- τ)H] (13)
The covariance matrix of wideband interferer signal is expressed as
R2=E [k (t- τ) k (t- τ)H] (14)
The covariance matrix of noise signal n (t) is expressed as
Rn=E [n (t) n (t)H] (15)
Wherein, E [] is covariance matrix, and H is conjugate transposition.
8. the design method of even power broadband signal Adaptive beamformer best initial weights according to claim 7, special
Sign is: substituting into the covariance matrix of useful signal, interference signal obtained in step 2, noise signal in the step 3
In linearly constrained minimum variance, optimal adaptive weight is obtained；Detailed process are as follows:
If the beam position of array is θ0, optimal adaptive weight vector w is the column vector of M dimension, optimal adaptive weight vector w
It is obtained based on LCMV criterion, i.e.,
Wherein μ is any one constant；α(f,θ0) be array guiding vector；
It enablesWhereinFor spherical wave received by i-th of array element, f is
Working frequency, then
It is the valuation of the interference plus noise covariance matrix of array output, is M × M dimension square matrix,By the association of broadband interference
The covariance matrix of variance matrix plus noise n (t) carries out K sampling and is estimated to obtain, expression formula are as follows:
Wherein K is sampling number, by α (f, θ0) andFormula (16) is brought into get uniform power spectrum density broadband signal digital wave is arrived
Beam forms optimal adaptive weight w.
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